A Novel Soft-Switching Converter for Switched Reluctance Motor Drives

Transcription

1 WEA TRANACTION on CIRCUIT and YTEM A Novel oft-wtchng Converter for wtched Reluctance Motor rves KUEI-HIANG CHAO epartment of Electrcal Engneerng Natonal Chn-Y Unversty of Technology 35, Lane 15, ec. 1, Chung-han Road, Tapng, Tachung TAIWAN, R.O.C. chaokh@ncut.edu.tw Abstract: - A hgh effcency converter for swtched reluctance motor (RM) drve s developed n ths paper. In the proposed converter, the power semconductor devce wth shorter swtchng tme s employed to mplement ts hgh-speed PWM swtches. And the soft-swtchng control s employed for further reducng ther swtchng losses. To acheve ths, an auxlary resonant crcut s added to the PWM swtch, and ts zero-voltage-transton (ZVT) soft swtchng s obtaned by applyng sutable swtchng sgnals to the man and auxlary swtches. No extra voltage and/or current sensors are requred. Havng derved the governng crcut equatons, a desgn procedure s proposed to systematcally fnd the consttuted components of the auxlary branch. As to the low-speed commutaton swtches, they are realzed usng the power devce havng low on-state voltage. Owng to the ablty of makng PWM swtchng control, the RM motor drve wth the proposed converter possesses good drvng performance. The performance of the desgned converter s demonstrated by some smulaton and expermental results. An approach for measurng the energy converson effcency of a RM drve s also proposed. Key-Words: wtched reluctance motor (RM), oft-swtchng converter, Zero voltage transton (ZVT), PWM, Effcency measurement, Hgh-effcency converter. 1 Introducton wtched reluctance motor (RM) possesses many advantages, such as rgd mechancal structure, brushless operaton, hgher converson effcency and power densty [1]. Moreover, ts converter crcut s smple and free from shoot-through fault [1-4]. However, n addton to the generaton of large acoustc nose and large torque rpple, ts developed torque characterstc s qute nonlnear. These factors may lmt the capablty of a RM n hgh-performance applcatons. urng the past decades, many researches have been done to mprove the performance of a RM drve. These nclude: motor desgn [], converter crcut [3,4], voltage boostng crcut [5,6], current waveform programmng [7,8], commutaton tunng [9]. And other related ssues, such as nose reducton, equvalent crcut development, current and speed controls, sensorless control, dgtal smulaton, etc. As generally recognzed, the drvng performance of a RM motor drve s sgnfcantly affected by ts employed converter and swtchng control. The whole motor drve performance s also affected by the converter effcency, partcularly for the battery-powered motor drve system. The conventonal hard-swtched converters possess nherent dsadvantages of generatng large swtchng losses, swtchng stresses and electromagnetc magnetc nterference (EMI). These problems can be effectvely reduced employng soft-swtchng technque to let the swtches have zero voltage and/or zero current swtchngs. oft-swtchng converters can be broadly categorzed nto resonant converters and zero voltage (current) (ZV(C)T) transton converters. The former types of converters possess larger lmtatons n crcut confguraton and PWM swtchng control. As to the latter, the crcuts can be formed from the conventonal ones by addng smple auxlary resonant branch. And the soft swtchng can be obtaned by applyng sutable swtchng sgnals to the man and auxlary swtches. Recently, there have been some soft-swtchng converters beng specfcally developed for powerng RMs. For the three-phase RM soft-swtchng converter developed n [10], an auxlary branch consstng of a Lesonant crcut and an auxlary swtch s used to let the man swtches have ZV at turn off. The converter presented n [11] s bascally an mproved crcut confguraton of the one n [10]. In whch, the auxlary swtch s not necessary. However, these types of converters suffer from the lmtatons: () the PWM swtchng control can not be performed; and () the swtchng frequency of converter s lmted, snce t must be synchronzed to IN: Issue 5, Volume 8, May 009

2 WEA TRANACTION on CIRCUIT and YTEM the resonant frequency of auxlary branch. In [1], a current-controlled quas-resonant unpolar converter usng thyrstors for RM s presented. Obvously, the PWM current control performance s also lmted. Another group of soft-swtchng converters [13,14] developed for RM belong to resonant C lnk converters. The one n [14] has lmted swtch voltage stress through usng the actvely clamped resonant C lnk. These converters also lack of PWM swtchng control capablty. In [15], the ZVT swtchng technque [16,17] s appled to let the swtches n a Mller converter possess ZV soft-swtchng characterstcs. However, only smulaton results are presented. In ths paper, a converter wth hgh effcency for RM s desgned and mplemented. Frst, a RM drve powered usng hard-swtched modfed Mller converter s establshed. Then the proposed converter s ntroduced. It s formed from the conventonal Mller s converter va sutable modfcatons n crcut and swtchng control. Each PWM swtch s augmented by an auxlary branch, and the ZVT soft swtchng s acheved by applyng sutable swtchng sgnals to the PWM man and auxlary swtches. No addtonal sensors are requred for makng the soft-swtchng control. Havng analyzed and derved the governng equatons of the converter n varous modes, the quanttatve desgn for the auxlary branch s made. As to the commutaton swtches, they are mplemented usng power devces wth lower on-state voltage. In makng the performance evaluaton of the developed converter, an effcency measurement approach s ntroduced. The smulaton and expermental results show that hgher energy converson effcency of the RM drve wth the desgned converter s obtaned, and the drvng control performance remans unchanged. Establshment of the RM rve Fg. 1 shows the establshed RM drve powered by the hard-swtched (n1)(n s the phase number of motor) Mller converter, whch uses two PWM swtches to lessen ther power burden. The RM, whch s manufactured by TAves Ltd., s rated as 8/6 4-phase, 1500rpm, 4kW. The C-lnk voltage s set as =310V. The permanent magnet synchronous generator (PMG) equpped wth swtched resstance s served as the dynamc load of the motor. For the converter, the four lower swtches are used for makng exctng commutaton of armature phase wndngs. Ther swtchng frequency s low, and the choce of power swtch s emphaszed n havng low on-state voltage. The MO-controlled thyrstor (MCT) may be a better choce. However, t s not popularly avalable commercally. Thus the IGBT IXGH41N60 (600V/75A, 0.45 μ s, 1.6V/41A) manufactured by IXY Company s adopted for mplementng these commutaton swtches. As to the upper two swtches, snce they are n charge of PWM swtchng control, the power swtch wth shorter swtchng tme s preferable for reducng the swtchng losses. Thus the IGBT IXGH39N60B1 (600V/75A, 0.μs, 1.8V/39A) s adopted here. And moreover, the ZVT soft-swtchng control wll be employed for further reducng ther swtchng losses. The control system shown n Fg. 1 s cascade-confgured consstng of speed and current loops. And the current-controlled PWM scheme s employed to obtan good wndng current trackng waveform. The commutaton sgnals ( 1 ~ 4 ) for lower swtches are yelded from the quadrature Hall sensng sgnals H A and H B. For ease of mplementaton, both the speed and current controllers are chosen to be the PI types: G c ω ( s) = 0.5, ( s) = 510 (1) s s Havng establshed the motor drve, some measured results are provded to show ts correctness and performance. Fgs. and show the measured wndng currents and ther commands of phase 1 at ( = 700rpm, RL = Ω) and ( = 1400rpm, R L = Ω ), respectvely. Fg. 3 shows the rotor speed responses and current commands due to step command change (700rpm 800rpm, R L =Ω) and step load resstance change (R L = Ω 13. Ω, = 700rpm ). Fg. 3 shows the results correspondng to ( 1400rpm 1500rpm, RL = Ω) and ( R L = Ω 304Ω, = 1400rpm ). The results shown n Fgs. and 3 ndcate that the establshed RM drve can normally be operated and possess satsfactory performances n wndng current trackng waveform and speed dynamc responses. G c 7 3 The Proposed Converter for RM rve Crcut confguraton of the proposed soft-swtchng converter s drawn n Fg. 4, whch s formed from the modfed Mller s converter shown n Fg. 1 by augmentng an auxlary resonant branch crcut for each PWM swtch to reduce ts swtchng losses. Each auxlary branch conssts of a swtch, a dode and a Lesonant crcut. The control system block dagram of the proposed soft-swtchng converter s shown n Fg. 4, whch s obtaned from Fg. 1 IN: Issue 5, Volume 8, May 009

3 WEA TRANACTION on CIRCUIT and YTEM by slght modfcaton. The ZVT soft-swtchng s obtaned by sutably delayng the turn-on nstant of the PWM swtchng sgnal of the man swtch, and wthn the delay perod the swtchng sgnal s appled to the auxlary swtch. Rectfer L d A 1 3 B 4 3φ AC 0V 60Hz C A L L 1 3 L L4 B H A H B EC RM ( Hall poston sensors) PMG R L A B Isolated gate drve crcuts H A Commutaton logc H B generator Current controller 3 4 v Current controller 3 v 3 Current controller 4 v 4 A B PWM modulator v 1 v v 3 v 4 Current controller K Gc () s = K p s e Phase wndng 3 current command 4 generator peed controller K e ω () ω G s K cω = pω s ω r Fg.1 Confguraton of the establshed hard-swtchng converter-fed RM drve ms Fg. Measured wndng currents and ther commands: ωr = 700rpm, R L = Ω ; =1400rpm, R L = The mechansm for generatng the delayed swtchng sgnals for man PWM swtches ( A and B ) and auxlary swtches ( Ar and Br ) s shown n Fg. 4(c). nce the delay tme s very short compared wth the PWM swtchng perod, the performance of the soft-swtchng converter s almost the same as those of conventonal converter. 3.1 Crcut Operaton and Governng Equatons The analyss s made for the partcular phase wndng, whch s beng performed the current-controlled PWM swtchng by the upper swtch A or B. The followng assumptons are reasonably made: () durng the PWM swtchng perod, the commutatng dode ( 1 ~ 4 ) s off, and one of the lower swtch s on. Ths leads to the crcut confguraton shown n Fg. 5; () snce the swtchng perod s very short, wthn whch the nput voltage and wndng current are all assumed to be constant,.e., o = Io and v =. Hence, the equvalent crcut of Fg. 5 s drawn n Fg. 5; () all the consttuted components are lossless; and (v) the resonant capactance s the sum of the parastc capactance of man swtch and the externally added capactance. IN: Issue 5, Volume 8, May 009

4 WEA TRANACTION on CIRCUIT and YTEM 700 rpm 5.5 A 700 rpm 5.7 A 145 rpm 7 A 500 ms 100 rpm 100 rpm PWM swtch can be dvded nto seven modes, crcut confguratons correspondng to these modes are shown n Fgs. 6 to 6(g). The waveforms of some key varables are sketched n Fg. 7. The operaton and the dervaton of governng equatons for each mode are brefly descrbed as followed. Mode 0 ( t6 t t0 ): As shown n Fg. 6, the man swtch and auxlary swtch r are all off. The wndng current flows to the load through the freewheelng dode. In ths case, = Io and v s =, t6 t t0. Mode 1 ( t0 t t1 ): As shown n Fg. 7, at t = t0, the man swtch s delayed and the auxlary swtch s arranged to turn on. Ths leads to the crcut shown n Fg. 6. urng ths mode, the constant voltage v = s appled across the resonant nductance to let ts current lnearly ncreased from zero: 1400 rpm 4.5 A 5.9 A 1 s 500 ms 100 rpm t) = ( t t ), t0 t t1 () L Lr ( 0 r Ths mode s termnated at t = t1 ( Lr ( t 1 ) = Io ), and the dode s naturally off wth ZC and ZV. The tme nterval of ths mode can be found to be: IoLr t = Δ 10 t1 t0 = (3) Mode ( t1 t t ): urng ths mode, the auxlary swtch r s on and s off leadng to the crcut shown n Fg. 6(c). The components and form a resonant crcut, and the state varables can be solved to be: 1400 rpm 4. A 8 rpm 100 rpm Lr = Io sn ω n ( t t1) Z (4) n vs = cosωn ( t t1), t1 t t where Lr Z Δ Δ 1 n =, ω n = C L C r r r Fg. 3 Measured speeds and current commands: ( =700rpm 800rpm, R L =Ω), (R L =Ω 13. Ω, =700rpm); ( =1400rpm 1500rpm, R L = Ω), (R L = Ω 304Ω, =1400rpm) The operaton of the proposed soft-swtchng 1 s When v s s decreased from to zero at t = t, ths mode s termnated. The tme nterval of ths mode s: t t t π 1 = Δ 1 = (5) The resonant nductor current at t = t can be found to be: Lr ( t ) = > (6) Z n IN: Issue 5, Volume 8, May 009

5 WEA TRANACTION on CIRCUIT and YTEM Note that ths value s larger than by V / Z. n Ar A As C Ar 1 3 Br B Bs C Br 4 C L Ar L Br L1 L3 L L 4 Ar A Br B Encoder F /V Converter peed controller e ω G cω (s) H A H B Phase wndng current command generator Commutaton logc generator Current controlled PWM schemes e 1 (s) G c The same as above The same as above The same as above q 1 q 3 q q 4 T A T B elay crcut elay (1) () A Ar B Br Hall poston sensors rvng sgnals for lower swtches Man swtchng sgnal A Man swtchng sgnal A Ar (c) Fg. 4 The proposed soft-swtchng converter-fed RM drve: converter crcut confguraton; control block dagram; (c) delay crcut for generatng the soft-swtchng control sgnals IN: Issue 5, Volume 8, May 009

6 WEA TRANACTION on CIRCUIT and YTEM r lnearly to ( t 4 ) = Io. From (8), one can fnd the tme nterval of ths mode r v sr s Lr t 34 = Δ t4 t3 = ( Io ) (9) V Z n v Lr r v L o Mode 5 ( t4 t t5 ): At t = t4, the dode r s naturally off wth ZC. The crcut of ths mode s shown n Fg. 6(f) and: I, v = 0, t4 t t5 (10) s = o s r v sr r s Mode 6 ( t5 t t6 ): As the man swtch s turned off (wth ZV) at t = t5, the operaton enters mode 6 wth the crcut beng drawn n Fg. 6(g). The constant current charges lettng ts voltage be lnearly ncreased. The governng equatons are: Lr r v I v t s o = t, v = vs, t5 t 6 (11) Cr As v s = at t 6, the dode conducts naturally (ZV). The operaton returns to mode 0 and repeats. Fg. 5 Per-phase crcut confguraton of the proposed soft-swtchng converter; equvalent crcut of. Mode 3 ( t t t3): Crcut confguraton of ths mode s drawn n Fg. 6(d). As the capactor voltage v s reduces to be slghtly negatve, the ant-parallel dode s of the man swtch s naturally on. It follows that the turn-on of man swtch after t = t wll possess ZV. The key varables durng ths mode are found to be: Lr = Lr ( t ), s =, t t t3 (7) Zn Mode 4 ( t3 t t4 ): At t = t3, and r are turned on and turn off, respectvely. The operaton enters mode 4 and the crcut becomes to those shown n Fg. 6(e). The key varables are: Lr = ( Io ) ( t t 3) Zn Lr (8) vs = 0, s = Io Lr, t3 t t4 At t = t4, ths mode ends. The current Lr (t) s lnearly decreased from ( Zn) to Lr ( t 4 ) = 0, meanwhle s decreased from s ( t 3 ) = Zn oft swtchng characterstcs: Accordng to the above analyss, the swtchng characterstcs of the consttuted actve components n the proposed ZVT soft-swtchng PWM swtch are summarzed as follows: Man crcut Auxlary branch wtch ( ) ode ( ) wtch ( r ) ode ( r ) Turn-on: ZV, ZC ZV ZC ZV, ZC Turn-off: ZV ZV, ZC none ZV, ZC 3. Crcut esgn The above analyss ndcates that the ZVT soft-swtchng of the man PWM swtch can be acheved f the delay tme satsfyng the followng condton: Io π td t = t10 t1 = Lr LrCr V (1) Under the known value of, the other parameters n (1) are determned as follows: () s chosen as the maxmum value of rated load current ( I ˆo, o = I max ). () Choosng a sutable value of, whch s equal to the sum of man swtch parastc capactance and the externally added capactance. IN: Issue 5, Volume 8, May 009

7 WEA TRANACTION on CIRCUIT and YTEM () t d : t s adequate to be chosen equal to 5%~10% of T s. If a lttle margn s set, then td = t tε = t10 t1 tε ( Iˆ o ) max π = Lr LrCr t V where t = 0.05T s ~0.1T s. (v) ε (13) : the maxmum value of resonant nductance =,max s the one solved from (13) by settng t be the maxmum value. r r Lr r s (d)mode 3: t ~ t3 r s r v sr s Lr r r Mode 0: t 6 ~ t0 (e) Mode 4: t 3 ~ t4 r r s r s Lr r r Mode 1: t 0 ~ t1 (f) Mode 5: t 4 ~ t5 r r s r s Lr r r v (c)mode : t 1 ~ t (g) Mode 6: t 5 ~ t6 Fg. 6 to (g): crcut confguratons correspondng to modes 0 to 6 IN: Issue 5, Volume 8, May 009

8 WEA TRANACTION on CIRCUIT and YTEM esgn example: The swtchng frequency of the desgn converter s chosen to be f s =5kHz. Accordng to the ratngs of the employed RM, the crcut components are desgned as follows: () The maxmum load current s I ˆomax =13.3A; () For the chosen IGBT (IXGH39N60B1), the parastc capactance s measured (usng HP 4194) to be nf at 5kHz, let Cr = nf for zero externally added capactance; () Let t = 0. 1T s =4.0 μ s and tε = 0. 01T s =0.4 μ s, then t d = 4.4μs ; (v) From (13) Lr =, max = 8.65 μ H, accordngly Lr = 0 μ H s chosen. The measured nductance of the desgned nductor s μ H at 5kHz. The system parameters are summarzed as: = 310V, Iˆo, max = 13.3A, Cr = nf, Lr = μ H. From (3) and (5), one can fnd that t10 = μ s and t1 = μ s. Thus t 10 t 1 =.3 μ s < t = 4 μ s. It should be noted that the smaller t and thus t d s chosen, the lower auxlary swtch conducton losses and the hgher effcency wll be obtaned. 3.3 mulaton Results Before performng the mplementaton, the effectveness of the desgned converter s frst confrmed va smulatons. The smulated waveforms of some key varables n the ZVT soft-swtchng PWM swtch of the desgned RM converter are shown n Fg. 8. The comparson between Fgs. 7 and 8 ndcates that the smulated waveforms are close to the predcted ones. The man swtch s turned on after ts voltage havng been equal to zero by the swtchng of auxlary swtch. Thus the ZVT soft swtchng s successfully acheved. 4.4μs t = 0.97μs 1.9 A ( = vcr ) 310V 13.4 A Fg. 7 ketched waveforms of key varables n the soft-swtchng PWM swtch 545 μs 550 μs 555 μs 560 μs 565 μs 570 μs 575 μs 580 μs 585 μs Fg. 8 mulated waveforms of key varables n the soft-swtchng PWM swtch. IN: Issue 5, Volume 8, May 009

9 WEA TRANACTION on CIRCUIT and YTEM 4 Implementaton and Performance Measurement of the esgned Converter 4.1 Implementaton The crcut components of the hard-swtched Mller converter part are the same as those descrbed n ec. and are not repeated here. As to the auxlary swtch, ts duty rato of conducted current s much smaller than those of man swtch. Thus the IGBT wth smaller ratngs can be employed. From the above analyss, the maxmum current of auxlary swtch s r Iˆo,max = 13.3A and the duty rato s t d / Ts = ( t tε ) / Ts = 4.4 μ s /40=11%. Accordngly, the power MOFET IRF840 (500V, I = 8A (contnuous), I M = 3A (pulsed)) s chosen for the auxlary swtch. Fg. 9 shows the swtchng sgnal generatng crcuts for producng the delayed PWM swtchng sgnals and pulsed swtchng control sgnals for the man and auxlary swtches. The orgnal PWM swtchng control sgnals are processed to yeld the delayed swtchng sgnals for the man swtches A and, and the pulsed swtchng sgnals for the B auxlary swtches T A 15V 5V 14 3k 10k 1 7 1/ 6 N7407N 15V Ar and Br. 4kΩ 4 TR1 1 5 TR1 3 Reset1 Q 6 11 Q C4098BCN p 15V T A Q A T A Q A 15V 16 1k A 1/ 4 C4081BCN 1k Ar 7 PWM man swtch under hard swtchng are plotted n Fgs. 11 and 11. The results n Fgs. 10 and 11 show that the measured waveforms of the desgned soft-swtchng converter are close to those by smulated and predcted ones. And the swtchng losses of the PWM swtches can be reduced va applyng the ZVT soft swtchng. r v s P s = v s v s Turn off loss 5 μs 6 V 6 V 500 V 1.5 A.5 kw 00 V 1.5 A T B 5V V 3k 10k 1/ 6 N7407N 7 15V kΩ TR1 1 TR1 Reset1 Q 6 Q 7 14 C4098BCN p 15V T B Q B T B Q B 15V 16 1k 1/ 4 C4081BCN 1k 7 B Br r 5 μs 6 V Fg. 9 oft swtchng sgnal generaton crcuts 6 V 4. Performance Evaluaton After mplementng the desgned soft-swtchng converter, ts performance s further confrmed expermentally. The wndng current trackng waveforms and speed dynamc responses are almost the same as those shown n Fgs. and 3, thus they are neglected here. Let the motor be operated stably at ( 700rpm, R L = 11Ω ), the measured voltage, current and power loss of the PWM man swtch are plotted n Fgs. 10 and 10. Fg. 10(c) shows the measured voltage and current of the auxlary swtch. Now let the auxlary branch be dsabled, the measured voltage, current and power loss of the v sr r (c) 5 μs 00 V 1.5 A Fg. 10 Measured key waveforms of the desgned soft-swtchng converter at ( =700rmp, R L =11Ω): man swtch voltage and current; man swtch power loss; (c) auxlary swtch voltage and current IN: Issue 5, Volume 8, May 009

10 WEA TRANACTION on CIRCUIT and YTEM The effcency mprovement by the proposed soft-swtchng converter s further confrmed quanttatvely. An approach for measurng the converson effcency of a RM drve s shown n Fg. 1. Through measurng the nput power of the converter and the powers of all wndngs usng the power analyzer PM100 manufactured by Voltech company, the effcency s obtaned by the followng defnton: Pout P1 P P3 P4 η = = (14) P P n n Let the swtchng frequences be 5 khz and 0kHz, Fgs. 13 and 13 plot the effcences yelded by the hard-swtched and soft-swtched converters at varous loads. The results ndcate that the effcency mprovement has been acheved by employng the desgned converter v s 6 V 500 V P n (W) ( f s = 5kHz) 1.5 A 9 5 μs = v s P s Turn on loss Turn off loss.5 kw v s 00 V 1.5 A ( f s = 0kHz) P n (W) Fg. 13 Effcences of the soft and hard swtchng converters: f s = 5kHz ; f s = 0kHz Fg. 11 Measured key waveforms of hard-swtchng converter at = 700rpm, R L = 11Ω ): man swtch voltage and current; man swtch power loss 3φ AC 0V 60Hz Rectfer L d P n C Power analyzer PM100 Phase1 Phase Phase 3 Phase4 P 1 Converter - fed RM PM100 L 1 P P3 P4 Fg. 1 The proposed effcency measurement approach 5 μs EC PMG R L 5 Conclusons A hgh effcency converter for powerng RM drve has been presented. For reducng the power losses generated n the Mller s converter, ts commutaton swtches are mplemented usng the IGBT wth lower on-state voltage. And the soft swtchng technque s utlzed to reduce the swtchng losses of ts PWM swtches. The soft-swtchng PWM swtch s formed from the conventonal swtch by augmentng an auxlary resonant branch. And the ZVT soft swtchng s obtaned by applyng sutable swtchng control sgnals to the man and auxlary swtches. The analyss and quanttatve desgn of the auxlary branch have been ntroduced. In makng the performance evaluaton, an effcency measurement approach for RM drve s proposed. The smulated and expermental results have confrmed that hgh effcency and good drvng performance of the RM IN: Issue 5, Volume 8, May 009

11 WEA TRANACTION on CIRCUIT and YTEM drve powered by the proposed soft-swtchng converter are obtaned. References [1] T. J. E. Mller, wtched Reluctance Motors and ther Control, Clarendon Press, Oxford, [] T. J. E. Mller, Optmal esgn of wtched Reluctance Motors, IEEE Transactons on Industral Electroncs, Vol. 49, No. 1, 00, pp [3]. Vukosavc and V. R. tefanovc, RM Inverter Topologes: a Comparatve Evaluaton, IEEE Transactons on Industry Applcatons, Vol. 7, No. 6, 1991, pp [4] C. Pollock and M. Barnes, Power Electronc Converters for wtched Reluctance rves, IEEE Transactons on Power Electroncs, Vol. 13, No. 6, Nov. 1998, pp [5] Y. G. essouky, B. W. Wllams and J. E. Fletcher, A Novel Power Converter wth Voltage-Boostng Capactors for a Four-Phase RM rve, IEEE Transactons on Industry Applcatons, Vol. 45, No. 5, 1998, pp [6] K. I. Hwu and C. M. Law, C-lnk Voltage Boostng and wtchng Control for wtched Reluctance Motor rves, IEE Proceedngs-Electrc Power Applcatons, Vol. 147, No. 5, 000, pp [7] I. Husan and M. Ehsan, Torque Rpple Mnmzaton n wtched Reluctance Motor rves by PWM Current Control, IEEE Transactons on Power Electroncs, Vol. 11, No. 1, 1996, pp [8].. chramm, B. W. Wllams and T. C. Green, Torque Rpple Reducton of wtched Reluctance Motors by Phase Current Optmal Proflng, IEEE 3rd Annual Power Electroncs pecalsts Conference, PEC '9 Record, Vol., 199, pp [9] J. J. Grbble, P. C. Kjaer and T. J. E. Mller, Optmal Commutaton n Average Torque Control of wtched Reluctance Motors, IEE Proceedngs-Electrc Power Applcatons, Vol. 146, No. 1, 1999, pp [10] Y. Mura, J. Cheng and M. Yoshda, New oft-wtched/wtched-reluctance Motor rve Crcut, IEEE Transactons on Industry Applcatons, Vol. 35, No. 1, 1999, pp [11] Y. Mura and J. Cheng, A mple oft-wtched wtched-reluctance Motor rve, IEEE Proceedng, IECON '98, Vol., 1998, pp [1] H. Le-Huy, K. lman and P. arouge, A Current-Controlled Quas-Resonant Converter for wtched-reluctance Motor, IEEE Transactons on Industral Electroncs, Vol. 38, No. 5, 1991, pp [13] G. Gallegos-Lopez, P. C. Kjaer, T. J. E. Mller and G. W. Whte, mulaton tudy of Resonant C Lnk Inverter for Current-Controlled wtched Reluctance Motors, IEEE Conference on Power Electroncs and rve ystems, Vol., 1997, pp [14]L. G. B. Rolm, W. I. uemtsu, E. H. Watanabe and R. Hantsch, evelopment of an Improved wtched Reluctance Motor rve Usng a oft-wtchng Converter, IEE Proceedngs- Electrc Power Applcatons, Vol. 146, No. 5, 1999, pp [15] T. W. Chng, K. T. Chau and C. C. Chan, A Novel Zero-Voltage oft-wtchng Converter for wtched Reluctance Motor rves, IEEE Proceedng, IECON '98, Vol., 1998, pp [16] G. Hua, C. Leu, Y. Jang and F. C. Lee, Novel Zero-Voltage-Transton PWM Converter, IEEE Transactons on Power Electroncs, Vol. 9, No., 1994, pp [17] K. H. Chao and C. M. Law, "A Three-Phase oft-wtchng Inverter for Inducton Motor rves, IEE Proceedngs-Electrc Power Applcatons, Vol. 148, No. 1, 001, pp IN: Issue 5, Volume 8, May 009